Complex Analysis

Complex Analysis
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作者: (小平邦彦)
2007-08
版次: 1
ISBN: 9780521809375
定价: 1600.20
装帧: 精装
开本: 16开
纸张: 胶版纸
页数: 416页
正文语种: 英语
  • Writtenbyamasterofthesubject,thistextwillbeappreciatedbystudentsandexpertsforthewayitdevelopstheclassicaltheoryoffunctionsofacomplexvariableinaclearandstraightforwardmanner.Ingeneral,theapproachtakenhereemphasisesgeometricalaspectsofthetheoryinordertoavoidsomeofthetopologicalpitfallsassociatedwiththissubject.Thus,Cauchy'sintegralformulaisfirstprovedinatopologicallysimplecasefromwhichtheauthordeducesthebasicpropertiesofholomorphicfunctions.Startingfromthebasics,studentsareledontothestudyofconformalmappings,Riemann'smappingtheorem,analyticfunctionsonaRiemannsurface,andultimatelytheRiemann-RochandAbeltheorems.Profuselyillustrated,andwithplentyofexamples,andproblems(solutionstomanyofwhichareincluded),thisbookshouldbeastimulatingtextforadvancedcoursesincomplexanalysis. KunihikoKodaira(1915-1997)workedinmanyareasincludingharmonicintegrals,algebraicgeometryandtheclassificationofcompactcomplexanalyticsurfaces.HeheldfacultypositionsatmanyuniversitiesincludingTokyo,Harvard,Stanford,andJohnsHopkins,andtheInstituteforAdvancedStudyinPrinceton.HewasawardedaFieldsmedalin1954andaWolfPrizein1984. 1. Holomorphic functions

    2. Cauchy's theorem

    3. Conformal mappings

    4. Analytic continuation

    5. Riemann's mapping theorem

    6. Riemann surfaces

    7. The structure of Riemann surfaces

    8. Analytic functions on a closed Riemann surface
  • 内容简介:
    Writtenbyamasterofthesubject,thistextwillbeappreciatedbystudentsandexpertsforthewayitdevelopstheclassicaltheoryoffunctionsofacomplexvariableinaclearandstraightforwardmanner.Ingeneral,theapproachtakenhereemphasisesgeometricalaspectsofthetheoryinordertoavoidsomeofthetopologicalpitfallsassociatedwiththissubject.Thus,Cauchy'sintegralformulaisfirstprovedinatopologicallysimplecasefromwhichtheauthordeducesthebasicpropertiesofholomorphicfunctions.Startingfromthebasics,studentsareledontothestudyofconformalmappings,Riemann'smappingtheorem,analyticfunctionsonaRiemannsurface,andultimatelytheRiemann-RochandAbeltheorems.Profuselyillustrated,andwithplentyofexamples,andproblems(solutionstomanyofwhichareincluded),thisbookshouldbeastimulatingtextforadvancedcoursesincomplexanalysis.
  • 作者简介:
    KunihikoKodaira(1915-1997)workedinmanyareasincludingharmonicintegrals,algebraicgeometryandtheclassificationofcompactcomplexanalyticsurfaces.HeheldfacultypositionsatmanyuniversitiesincludingTokyo,Harvard,Stanford,andJohnsHopkins,andtheInstituteforAdvancedStudyinPrinceton.HewasawardedaFieldsmedalin1954andaWolfPrizein1984.
  • 目录:
    1. Holomorphic functions

    2. Cauchy's theorem

    3. Conformal mappings

    4. Analytic continuation

    5. Riemann's mapping theorem

    6. Riemann surfaces

    7. The structure of Riemann surfaces

    8. Analytic functions on a closed Riemann surface
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